Abstract
Multiparty quantum cryptography based on distributed entanglement will find its natural application in the upcoming quantum networks. The security of many multipartite device-independent (DI) protocols, such as DI conference key agreement, relies on bounding the von Neumann entropy of the parties' outcomes conditioned on the eavesdropper's information, given the violation of a multipartite Bell inequality. We consider three parties testing the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality and certify the privacy of their outcomes by bounding the conditional entropy of a single party's outcome and the joint conditional entropy of two parties' outcomes. From the former bound, we show that genuine multipartite entanglement is necessary to certify the privacy of a party's outcome, while the latter significantly improve previous results. We obtain the entropy bounds thanks to two general results of independent interest. The first one drastically simplifies the quantum setup of an $N$-partite Bell scenario. The second one provides an upper bound on the violation of the MABK inequality by an arbitrary $N$-qubit state, as a function of the state's parameters.
Highlights
Stimulated by data-security concerns and by commercial opportunities, several companies and governments are increasingly investing resources in quantum-cryptography technologies [1,2]
We focus on the Mermin-Ardehali-BelinskiiKlyshko (MABK) inequality [57,58,59] and derive an analytical bound on the maximal violation of the MABK inequality yielded by rank-one projective measurements on an given N -qubit state
We provide a heuristic argument for which full-correlator Bell inequalities, such as the MABK inequality, are unlikely to be employed in any DI conference-key agreement (DICKA) protocol
Summary
Stimulated by data-security concerns and by commercial opportunities, several companies and governments are increasingly investing resources in quantum-cryptography technologies [1,2]. Eve’s uncertainty is quantified by appropriate conditional von Neumann entropies [6,33,34,38] of the effective quantum state shared by the parties in a generic round of the protocol. We follow an analytical approach that reduces the degrees of freedom of the generic state shared by the parties without loss of generality, thereby allowing a direct minimization of the conditional von Neumann entropy This can result in a tight bound of Eve’s uncertainty, in longer secret bitstrings and higher noise tolerance for the DI protocol. Our results on the state reduction in a multipartite DI scenario and on the MABK violation upper bound, allow us to quantify Eve’s uncertainty about the parties’ outcomes when three parties, Alice, Bob, and Charlie, test the MABK inequality (see Fig. 1). The derived bound can be employed in proving the security of DI global randomness generation schemes
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